Advanced optimal GWO-PID controller for DC motor

The current work aims to use traditional control algorithms and advanced optimization algorithms that was chosen for its ease of control and the possibility of using it in many industrial applications. By setting the appropriate specifications for the simulation model and after conducting the planned tests that simulate different applications of the motor’s work within electrical systems, the results proved to obtain good performance of the motor’s work, better response, high accuracy, in addition to the speed. The goal is to design and tune a proportional–integral–derivative (PID) controller by grey wolf optimization (GWO) using T.F for a direct current (DC) motor. To adjust the parameters of the traditional controllers using the optimum advanced, an appropriate mechanism and technology from the advanced optimization techniques were chosen, as the gray wolf technology algorithm was chosen as an optimization technique and integral time absolute error (ITAE) to adjust the parameters of the traditional PID controller.


INTRODUCTION
Electric motors are generally used in many systems, including household, military, medical and industrial [1], [2].Direct current (DC) motors are considered one of the most important electric motors [3]- [5].They have specifications that make their choice to move many machines within different applications [6]- [8].It is the most appropriate technically with high performance and spatiality, occupying less place due to its small size [9]- [11].DC motors have occupied a wide range of application fields due to their high performance.DC motors include conventional DC and brushless DC electric motor (BLDC) [12]- [14].
Conventional control systems handle errors resulting from the work of linear systems, any adjustment process for their parameters according to the linear system is designed [15]- [17].An algorithm is developed to suit the system that needs a control unit to improve its performance [18]- [20].In order to improve the performance of the work of linear systems and the shortcomings of traditional performance [21]- [23].Many solutions were found, including the advanced optimization [24]- [26].They simulate the hunter and prey and the iteration process as a result of similar cases and experience, including the genetic algorithm (GA) and Particle swarm optimization (PSO) as well as the wolves grey wolf optimization (GWO) and there are other ways [27]- [29].
In the current work, the GWO algorithm was chosen to adjust parameters the traditional proportional-integral-derivative (PID) controller to improve the working performance of the DC motor.To control the motor speed no it is necessary to specify a target function such as integral time absolute error (ITAE).The work of this type of techniques depends on the creation of a random number of the hunting group and the target function determines the hunting behavior and works to estimate the location of the prey through iterative processes to obtain the optimal location of the prey.

DC MOTOR AND SIMULATION MODEL
The electric motor works to produce mechanical energy through the torque arising from the passage of an electric current in the coils of the motor [30]- [32].First, which in turn acts as an influence in the magnetic circuit in the motor and thus produces a magnetic driving force.Second, which in turn generates a torque to rotate the moving part [33]- [35] which is the rotating part of the electric motor, which produces kinetic energy or mechanical [36]- [38].The electric motor has special specifications that make the selection process for any application easy [39]- [41].Such as rotational speed, number of poles, capacity, current, voltage, etc. according to the manufacturer, and each quantity has a symbol and amount.Table 1 represents the specifications of a DC motor that is intended to perform a computer simulation.To represent it mathematically first and to find the transformation function which is used in building the simulation model.A working algorithm is developed to simulate the operation of the engine first without quantum units.Secondly, the engine is run with the traditional control unit and compared with the previous case.Third, the simulations are carried out with the optimized advanced technique and the comparison with the previous cases.After the simulation, it is possible to work on the appropriate design to control the work of the electric motor by setting an algorithm for better performance, higher speed and accuracy in quality to reach a state close to ideal in performance.In Figure 1 show the simple model for DC motor.In Figure 2 show the block diagram for DC motor at Tf = 0 (no load).In Figure 3 show the block diagram for DC motor with Tf (load).The electric motor has an electric part and it can be put into a mathematical model with equations through which the theoretical specifications can be obtained and the ideal calculations are calculated through it.Equation 1 and Equation 2 include both voltage and power, respectively.The electric motor has a mechanical second part that can be represented in equation 3 and equation 4 for speed and torque.Straight [42]- [44].
Where, P =shaft power, T= motor torque P=500*0.108=54watt Where, ea(t)= armature terminal voltage, ia(t)= armature current, Ra= armature resistance, La= armature inductance, eb(t)= back emf Where, KT = torque constant, Tf= static friction torque, Jm= rotational inertia, Bm = viscous friction The mathematical model of the electric motor can also be described by the mathematical equations: Lap. Tra. of electrical equation: E a (s) = L. s.I a (s) + R a + I a (s) Mechanical equation: Lap. Tra. of mechanical equation: Electromechanical relationships: Lap. Tra. of electromechanical relationships:e b (s A transfer function for a DC motor as show in equation 13 [43]. T. Ffor DC motor = Hierarchical algorithm, as shown in Figure 4, is called wolf algorithm and can be represented by categories that include the leader, who is from the first level to the top of the hierarchy and is called alpha (a).This category is concerned with making decisions such as the spatial environment for living and hunting and can be male or female or both.The second category is a body considered in the second level of the hierarchy Hierarchical duty helps the first category to make some decisions and is called Beta (ꞵ).The third category is lower than its predecessors in terms of hierarchy called delta (δ), where it is considered a category subject to the orders of other groups and has a role to play, which is being a scapegoat.Below the pyramid is the lowest rank category, the fourth, which is the category of sheikhs, which performs the functions of guard and scouts.It is considered dominant over its predecessor, Omega (ꙍ), but is subject to both alpha and betas.In Figure4 show the hierarchy of GWO.Also, the GWO had flow chart that show in Figure 5.In Figures 10-12 the simulation model for DC motor.First the simulation model for DC motor without controller as show in Figure 10.Second the simulation model for DC motor with PID controller as show in Figure 11.Then, simulation model for DC motor with GWO-PID controller as show in Figure 12.
To improve the performance of the work of systems asks for the search for performance indications, which are placed to be indications to improve the performance of systems.To design appropriate controllers for any system are tested through one or more performance indications for a high effective system and within the required specifications.These indications can be recognized through the following equations for each type: i) Integral absolute error (IAE) as show in (15).Also in Figure 6

Simulation model for DC motor with variable speed
In this section there are three parts, in Figures 13-15 simulation model for DC motor of variable speed, first the simulation model for DC motor of variable speed without controller as show in Figure 13.Second, the simulation model for DC motor of variable speed with PID controller as show in Figure 14.Last, the simulation model for DC motor of variable speed with GWO-PID controller as show in Figure 15.

Simulation results of DC motor with variable speed
In this section there are three parts, in Figures 19-21 simulation results for DC motor of variable speed.First the simulation response for DC motor of variable speed without controller as show in Figure 19.Second the simulation response for DC motor of variable speed with PID controller as show in Figure 20.Third the simulation response for DC motor of variable speed with GWO-PID controller as show in Figure 21.In Figure 22 show the ITAE with each iteration.In Figure 23 show the step response.In Figure 24 show the wondow of T.F code for DC motor.In Figure 25 show the wondow of code for GWO-PID.

CONCLUSION
The current study was conducted by simulating the operation of a DC motor with working conditions for three cases that were selected and suggested to verify the preference for using the optimal advance and compare it with the two cases of no control systems.Others with the presence of control using the traditional system, a traditional control unit.The results demonstrated the superiority of the optimum advanced over the traditional progress unit in terms of response speed, time to reach a stable state, accuracy and quality.To adjust the parameters of the traditional controllers using the optimum advanced, an appropriate mechanism and technology from the advanced optimization techniques were chosen, as the Gray wolf technology algorithm was chosen as an optimization technique and ITAE to adjust the parameters of the traditional PID controller.The response speed, high accuracy, stability time and overtaking are higher and lower compared to different cases of working conditions that simulate real time.

Figures 13 .
Figures 13.Simulation model for DC motor of variable speed without controller

Figure 19 .Figure 20 .Figure 21 .
Figure 19.Simulation response for DC motor of variable speed without controller

Table 2 .
Simulation results with different algorithm